Slant short-period grating

ABSTRACT

There is provided a slant short-period grating which is obtainable by irradiating light onto an optical fiber whose core is formed from quartz glass to which has been doped a photosensitive dopant that changes a refractive index of the quartz glass by light irradiation, and whose clad has one or two or more layers with at least the layer that is adjacent to the core being a photosensitive layer formed from quartz glass to which has been doped a photosensitive dopant that changes a refractive index of the quartz glass by light irradiation. In this slant short-period grating a grating portion is formed by changing the refractive index of the photosensitive layer of the clad and the core at a predetermined grating period along a longitudinal direction of the optical fiber by a predetermined slant angle. The diameter of the core is set to 5 μm or more, and the relative photosensitivity ratio of the core relative to the photosensitive layer of the clad that is adjacent to the core is designed so as to satisfy a predetermined formula. As a result, in the wavelength spectrum of transmitted light, loss peaks are obtained in a narrow frequency band.

TECHNICAL FIELD

The present invention relates to a slant short-period grating used as anoptical filter or the like in the field of optical communications andthe like.

This application is based on Patent Application No. 2000-183796 filed inJapan, the contents of which are incorporated herein by reference.

BACKGROUND ART

An optical fiber grating is one example of a fiber type of opticalfilter. There are long-period grating (LPG) and short-period grating(SPG) types of optical fiber grating.

Conventionally, an optical fiber grating is formed by changing therefractive index of a core at a predetermined grating period in thelongitudinal direction of the core. Note that the term grating periodrefers to the period of this refractive index change. An LPG gratingperiod is approximately several hundred μm.

In LPG, in a grating section in which a change in the refractive indexis formed, light of a predetermined wavelength region from the incidentlight is coupled with a forward clad mode that moves forward in the samedirection as the incident light, and transmitted light is obtained fromwhich the light of this wavelength region has been lost.

In contrast to this, in SPG, the grating period is approximately onehalf to one third the wavelength of the light. Namely, if the operatingwavelength is in the vicinity of 1.55 μm, then a value of, for example,approximately one third of this is set. As a result, the light of apredetermined wavelength region, from among waveguide modes that arepropagated along the core of an optical fiber, is reflected and coupledwith a reflection mode, and transmitted light is obtained from whichthis light has been lost.

LPG has the advantage that there are no micro ripples that causedegradation in the signal waveform. The term micro ripples refers tominute fluctuations in the wavelength spectrum of transmitted light whenthe horizontal axis is the wavelength and the vertical axis is thetransmittance. Therefore, LPG enables a smooth characteristic to beobtained in the wavelength spectrum. A further advantage is thatreflected light is practically non-existent.

However, LPG has the disadvantage of it being difficult to obtainarbitrary transmission characteristics due to the difficulty ofadjusting the transmission characteristics.

In SPG, in addition to the amount of change in the refractive index ofthe grating portion and the grating period, by employing a chirpedgrating in which the grating period is changed by being graduallyextended or shortened in the longitudinal direction thereof, it ispossible to widen the wavelength region of the lost light and to adjustthe intensity of the lost light, and it is possible to obtain arbitrarytransmission characteristics comparatively freely.

However, in SPG, multiple reflections are generated by the action ofreflected light, and as a result, micro ripples are generated in thewavelength spectrum of the transmitted light creating the problem of itnot being possible to obtain smooth wavelength spectrum characteristics.There is also the problem that there is a large amount of reflectedlight.

For these reasons, recently, the freedom of design allowed by SPG hasbeen used to further the development of slant SPG in which it is evenmore difficult for micro ripples to occur.

FIG. 24 is a side cross-sectional view showing an example of a slantSPG. A description will now be given of the production method for thisslant SPG

The symbol 1 in the drawing is a core. An optical fiber is formed byproviding a clad 2 having a lower refractive index than the core 1 onthe outer periphery of the core 1.

The core 1 and clad 2 are both formed from quartz glass. Aphotosensitive dopant that raises the refractive index of quartz glasswhen light of a specific wavelength is irradiated onto it is doped tothe core 1. Normally, germanium is used as the photosensitive dopant.The refractive index is raised when ultraviolet light of approximately240 nm is irradiated onto the germanium doped quartz glass.

Accordingly, when light is irradiated at a predetermined grating periodin the longitudinal direction of the core 1 from one side surface of theoptical fiber by the interposition of a phase mask or the like, therefractive index of that portion of the core 1 receiving the irradiatedlight is raised so that a grating portion 4 in which a plurality of highrefractive index portions 3, 3, . . . are arranged at a predeterminedgrating period is obtained.

The high refractive index portions 3, 3, . . . are formed on aninclination so as to cut across the core 1 without being orthogonal tothe center axis B of the core 1. Moreover, a plurality of highrefractive index portions 3, 3, . . . are arranged parallel to eachother in the longitudinal direction of the core 1. The direction of aline A that is perpendicular to a high refractive index portions 3 isknown as the grating direction. Alternatively, this direction is knownas the lattice vector direction of the grating portion.

An angle θ between the grating direction A and the center axis B of thecore 1 is known as the slant angle. The size of the inclination of therefractive index portions 3 is represented by this angle θ. Note that innormal SPG the grating direction matches the center axis of the core 1so that the angle θ is zero.

As a result, light that moves along the core 1 in the same direction asthat of the incident light and whose waveguide mode is reflected by thegrating portion 4 is irradiated onto the clad 2, and couples with areverse clad mode that is moving in the opposite direction to theincident light. Namely, because it does not couple with a reflectionmode that moves in reverse along the core 1, it is difficult formultiple reflections to occur. It is therefore possible to reduce theintensity of the micro ripples obtained in the wavelength spectrum.

FIGS. 25A, 25B, 26A, and 26B show wavelength spectrums for various slantangles.

Because the waveguide mode couples with a plurality of reverse cladmodes, in the waveguide spectrum a plurality of loss peaks are alignedadjacent to each other.

If the slant angle is increased from 0 degrees to 2.9 degrees, 4degrees, and 5.8 degrees, then the coupling with the reflection mode ofthe waveguide modes is smallest at 4 degrees. When the slant angle isfurther increased to 5.8 degrees, then the coupling begins to increaseagain. Namely, periodic characteristics are demonstrated in whichcouplings with reflection modes repeatedly increase and decrease as theslant angle increases.

The angle at which the couplings with reflection modes first reach theminimum value is known as the reflection suppression angle (4 degrees inthis example, as is shown in FIG. 26A).

In slant SPG if the slant angle is set in the vicinity of the reflectionsuppression angle, it is possible to reduce the effects of microripples.

However, in a slant SPG that uses a typical single mode optical fiberthat has a core and clad having a lower refractive index than the coreprovided on the outer periphery of the core, with the core being formedfrom germanium doped quartz glass while the clad is formed from purequartz glass, if the slant angle is set in the vicinity of thereflection suppression angle, the region where the waveguide modecouples with a clad mode is extended, creating the drawback that it isnot possible to obtain a steep wavelength spectrum.

FIG. 27 shows an example of a wavelength spectrum of slant SPGtransmitted light obtained when, in the core of the above type oftypical single mode optical fiber, the slant short period gratingportion is formed such that the slant angle is in the vicinity of thereflection suppression angle at a fixed grating period. The loss region(the region of peak loss) reaches as far as 20 nm or more.

Furthermore, in a slant SPG it is possible in some cases to makedivisions into main bands, which are wavelength regions where a largeloss peak is obtained in the transmitted light wavelength spectrum, andside bands, which are small wavelength regions that appear on the shortwavelength side of the main bands. There are also cases in whichunnecessary ghost mode peaks are present in portions of the longwavelength side of the main band loss peaks, and cases in which there isa large side band transmission loss that becomes noise that appears tobe parallel to the main band loss peaks.

If ghost peaks are present, or if there is a large side bandtransmission loss, then essentially it is not possible to make the lossband sufficiently narrow, and, in some cases, a steep wavelengthspectrum cannot be obtained.

Moreover, even if the same light exposure, namely, the same change inthe refractive index is provided, if the area of the main band of thetransmission loss (referred to below on occasion as “transmission lossarea”) is small, it is necessary to lengthen the exposure in order toobtain the same filter characteristics. This becomes a drawback duringproduction.

Thus, in slant SPG, various problems exist such as difficulty ofobtaining a steep wavelength spectrum, reducing the ghost mode peaks,reducing side band transmission loss, and increasing the transmissionloss area. Accordingly, in some cases, it is difficult to obtain thedesired characteristics, and there is still an insufficient degree offreedom allowed when designing optical characteristics. In particular,it has often been difficult to obtain a narrow loss band.

Slant SPG is used, for example, to equalize the wavelength—gaincharacteristics of erbium (Er) doped optical fiber amplifiers. Slant SPGthat allows a variety of designs for dealing with the opticalcharacteristics of the gain—wavelength characteristics of these Er dopedoptical fiber amplifiers is desirable. When slant SPG is used for the Erdoped optical fiber amplifiers, it is preferable for the ghost modes andthe side band transmission loss of the slant SPG not to generateproblems.

The present invention was conceived in view of the above circumstancesand it is one object of the present invention is to provide a slant SPGthat enables the free designing of optical characteristics.

Specifically, one object of the present invention is to provide a slantSPG having a narrow loss band in a transmitted light wavelengthspectrum. In addition, one object of the present invention is to providea slant SPG that has a greater transmission loss area using the samerefractive index change.

In addition, one object of the present invention is to provide a slantSPG in which ghost mode peaks are decreased. In addition, one object ofthe present invention is to provide a slant SPG that enables a reductionin side band transmission loss to be achieved.

DISCLOSURE OF INVENTION

In order to achieve the above aims, in the present invention theinventions described below are proposed.

The first aspect of the present invention is a slant short-periodgrating which is obtainable by irradiating light onto an optical fiberhaving a core and a clad provided on an outer periphery of the core, thecore being formed from quartz glass to which has been doped aphotosensitive dopant that changes a refractive index of the quartzglass by light irradiation, and the clad having one or two or morelayers with at least the layer that is adjacent to the core being aphotosensitive layer formed from quartz glass to which has been doped aphotosensitive dopant that changes a refractive index of the quartzglass by light irradiation, and thereby a grating portion is formed bychanging the refractive index of the photosensitive layer of the cladand the core at a predetermined grating period along a longitudinaldirection of the optical fiber by a predetermined slant angle,

wherein a diameter of the core is 5 μm or more;

wherein a relative photosensitivity ratio of the core relative to thephotosensitive layer of the clad that is adjacent to the core satisfiesFormula (1) below:

0.2−0.1·(V−1.7)≦P≦0.1a{0.41−0.33·(V−1.7)}  (1)

in Formula (1), a is the diameter of the core in units of μm, V is astandardized frequency, and P is the relative photosensitivity ratio ofthe core relative to the photosensitive layer of the clad that isadjacent to the core; and

wherein the slant angle is set to such an angle that loss due tocoupling of a waveguide mode with a reflection mode is minimum.

The second aspect of the present invention is a slant short-periodgrating, in the slant short-period grating according to first aspect ofthe invention, wherein the diameter of the core is 7 μm or more.

The third aspect of the present invention is a slant short-periodgrating, in the slant short-period grating according to first aspect ofthe invention, wherein the relative photosensitive ratio of the core is0.1 to 0.4.

The fourth aspect of the present invention is a slant short-periodgrating, in the slant short-period grating according to first aspect ofthe invention, wherein an outer diameter of the photosensitive layer ofthe clad is four times or more the diameter of the core.

The fifth aspect of the present invention is a slant short-periodgrating, in the slant short-period grating according to first aspect ofthe invention, wherein the diameter of the core is 12 μm or less.

The sixth aspect of the present invention is a slant short-periodgrating, in the slant short-period grating according to first aspect ofthe invention, wherein a comparative refractive index difference betweenthe core and the clad is 0.5% or less.

The seventh aspect of the present invention is a slant short-periodgrating, in the slant short-period grating according to first aspect ofthe invention, wherein aluminum or phosphorous is doped to the core.

The eighth aspect of the present invention is a slant short-periodgrating which is obtainable by irradiating light onto an optical fiberhaving a core and a clad provided on an outer periphery of the core, theclad having one or two or more layers with at least one layer being aphotosensitive layer formed from quartz glass to which has been doped aphotosensitive dopant that changes a refractive index of the quartzglass by light irradiation, and thereby a grating portion is formed bychanging the refractive index of the photosensitive layer at apredetermined grating period along a longitudinal direction of theoptical fiber by a predetermined slant angle,

wherein a relative photosensitivity ratio of the core relative to thephotosensitive layer of the clad that has the highest photosensitivitysatisfies Formula (2) below:

P≦m ₁(V−2)+m ₂

m ₁=0.0041667a ⁴−0.13519a ³+1.6206a ²−8.511a+16.291  (2)

m ₂=−0.00832827a ²+0.18344a−0.6912

however, when P equals 0 or smaller or is imaginary number, P is 0

in Formula (2), a is the diameter of the core in units of μm, V is astandardized frequency, and P is the relative photosensitivity ratio ofthe core relative to the photosensitive layer of the clad that has thehighest photosensitivity.

The ninth aspect of the present invention is a slant short-periodgrating which is obtainable by irradiating light onto an optical fiberhaving a core and a clad provided on an outer periphery of the core, theclad having one or two or more layers with at least one layer being aphotosensitive layer formed from quartz glass to which has been doped aphotosensitive dopant that changes a refractive index of the quartzglass by light irradiation, and thereby a grating portion is formed bychanging the refractive index of the photosensitive layer at apredetermined grating period along a longitudinal direction of theoptical fiber by a predetermined slant angle,

wherein a relative photosensitivity ratio of the core relative to thephotosensitive layer of the clad that has the highest photosensitivitysatisfies Formula (3) below:

P≧(V−1.7868)^(0.048522)+0.17416V−1.121  (3)

however, when P equals 0 or smaller or is imaginary number, P is 0

in Formula (3), a is the diameter of the core in units of μm, V is astandardized frequency, and P is the relative photosensitivity ratio ofthe core relative to the photosensitive layer of the clad that has thehighest photosensitivity.

The tenth aspect of the present invention is a slant short-periodgrating which is obtainable by irradiating light onto an optical fiberhaving a core and a clad provided on an outer periphery of the core, theclad having one or two or more layers with at least one layer being aphotosensitive layer formed from quartz glass to which has been doped aphotosensitive dopant that changes a refractive index of the quartzglass by light irradiation, and thereby a grating portion is formed bychanging the refractive index of the photosensitive layer at apredetermined grating period along a longitudinal direction of theoptical fiber by a predetermined slant angle,

wherein a relative photosensitivity ratio of the core relative to thephotosensitive layer of the clad that has the highest photosensitivitysatisfies Formula (4) below:

P≧m1(a−m2)^(m3)

m1=−0.28947+0.17702V

m2=−344.28+543.53V−272.8V ²+44.494V ³  (4)

m3=0.96687−0.24791V

however, when P equals 0 or smaller or is imaginary number, P is 0

in Formula (4), a is the diameter of the core in units of μm, V is astandardized frequency, and P is the relative photosensitivity ratio ofthe core relative to the photosensitive layer of the clad that has thehighest photosensitivity.

The eleventh aspect of the present invention is a slant short-periodgrating, in the slant short-period grating according to any of theeighth to tenth aspects of the invention, wherein the slant angle is setsuch that loss due to coupling of a waveguide mode with a reflectionmode is minimum.

The twelfth aspect of the present invention is a slant short-periodgrating, in the slant short-period grating according to any of theeighth to tenth aspects of the invention, wherein the relativephotosensitivity ratio of the core relative to the photosensitive layeris 0.2 or more.

The thirteenth aspect of the present invention is a slant short-periodgrating, in the slant short-period grating according to any of theeighth to tenth aspects of the invention, wherein the grating period isa chirped pitch, and the chirping ratio of the grating period is 20nm/cm or less.

The fourteenth aspect of the present invention is a slant short-periodgrating, in the slant short-period grating according to any of the firstto tenth aspects of the invention, wherein a bend loss of an opticalfiber under conditions of a wavelength of 1,550 nm and a windingdiameter of 60 mm, is 1 dB/m or less.

The fifteenth aspect of the present invention is a slant short-periodgrating, in the slant short-period grating according to any of the firstto tenth aspects of the invention, wherein a bend loss of an opticalfiber in conditions of a wavelength of 1,550 nm and a winding diameterof 40 mm is 0.1 dB/m or less.

The sixteenth aspect of the present invention is a slant short-periodgrating, in the slant short-period grating according to any of the firstto tenth aspects of the invention, wherein a mode field diameter of awaveguide mode of the optical fiber in an operating wavelength of theslant short-period fiber grating is 15 μm or less.

The seventeenth aspect of the present invention is a slant short-periodgrating, in the slant short-period grating according to any of the firstto tenth aspects of the invention, wherein the outer diameter of thephotosensitive layer is 1.5 times or more the size of the mode fielddiameter of a waveguide mode of the optical fiber in an operatingwavelength of the slant short-period fiber grating

The eighteenth aspect of the present invention is a slant short-periodgrating, in the slant short-period grating according to any of the firstto tenth aspects of the invention, wherein the outer diameter of thephotosensitive layer is 60 μm or less.

The nineteenth aspect of the present invention is a slant short-periodgrating, in the slant short-period grating according to any of the firstto tenth aspects of the invention, wherein the length of the gratingportion is 1 to 100 mm.

The twentieth aspect of the present invention is an optical amplifiermodule comprising the slant short-period grating according to any of thefirst to tenth aspects and an optical amplifier, wherein gainequalization of the optical amplifier is performed by the slantshort-period grating.

The twenty-first aspect of the present invention is an optical amplifiermodule, in the optical amplifier module according to the twentiethaspect, wherein the optical amplifier is an erbium doped optical fiberamplifier.

The twenty-second aspect of the present invention is an opticalcommunication system that employs the optical amplifier module accordingto the twentieth aspect.

The twenty-third aspect of the present invention is a manufacturingmethod for a slant short-period grating in which a slant short-periodgrating is designed and manufactured such that the conditions describedin any of the first to tenth aspects are satisfied.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a graph showing design conditions for an optical fiberrefractive index profile and a relative photosensitivity ratio profile.

FIG. 2 is a graph showing an example of a result of a calculation ofcoupled wavelength and transmission loss in the first embodiment.

FIGS. 3A and 3B are graphs showing a relationship between a relativephotosensitivity ratio of a core and a main band frequency band, and arelationship between a relative photosensitivity ratio of a core and aside band/main band loss ratio according to the first embodiment.

FIGS. 4A and 4B are graphs showing a relationship between a relativephotosensitivity ratio of a core and a main band frequency band, and arelationship between a relative photosensitivity ratio of a core and aside band/main band loss ratio according to the first embodiment.

FIGS. 5A and 5B are graphs showing a relationship between a relativephotosensitivity ratio of a core and a main band frequency band, and arelationship between a relative photosensitivity ratio of a core and aside band/main band loss ratio according to the first embodiment.

FIG. 6 is a graph showing the electric field strength of a clad modeforming a side band.

FIG. 7 is a graph showing ranges of three parameters that fulfill thecharacteristics of the slant SPG of the first embodiment.

FIG. 8 is a graph showing an example of a wavelength spectrum oftransmitted light of the slant SPG of the first embodiment.

FIG. 9 is a graph showing a result of a calculation of a relationshipbetween an effective refractive index and a coupling constant in theslant SPG of the second embodiment.

FIG. 10 is a graph showing an example of the relationship betweenwavelength-transmission loss characteristics in the second embodiment.

FIGS. 11A and 11B are graphs showing an example of a relationshipbetween a relative photosensitivity ratio of a core and a main bandfrequency band in the second embodiment.

FIGS. 12A and 12B are graphs showing an example of a relationshipbetween a relative photosensitivity ratio of a core and a main bandfrequency band in the second embodiment.

FIGS. 13A and 13B are graphs showing an example of a relationshipbetween a relative photosensitivity ratio of a core and a main bandfrequency band in the second embodiment.

FIGS. 14A and 14B are graphs showing an example of a relationshipbetween a relative photosensitivity ratio of a core and integral valuesin the second embodiment.

FIGS. 15A and 15B are graphs showing an example of a relationshipbetween core wavelength and transmission loss in the second embodiment.

FIG. 16 is a graph showing an example of a wavelength spectrum of aslant SPG in which ghost mode peaks are present.

FIGS. 17A and 17B are graphs showing an example of a relationshipbetween normalized frequencies and a coupling constant ratio in thesecond embodiment.

FIGS. 18A and 18B are graphs showing an example of a relationshipbetween normalized frequencies and a coupling constant ratio in thesecond embodiment.

FIGS. 19A and 19B are graphs showing an electric field distribution ofLP11 mode and waveguide mode.

FIGS. 20A and 20B are graphs showing an example in which ghost modepeaks are present and an example in which ghost mode peaks are notpresent in the second embodiment.

FIGS. 21A and 21B are graphs showing a core diameter—side band/main bandloss ratio in the second embodiment.

FIGS. 22A and 22B are graphs showing a core diameter—side band/main bandloss ratio in the second embodiment.

FIGS. 23A and 23B are graphs showing an example when a side band islarge and an example when a side band is small in the second embodiment.

FIG. 24 is an explanatory view showing an example of the structure of aslant SPG.

FIGS. 25A and 25B are graphs showing examples of a slant SPG wavelengthspectrum when the slant angle is changed.

FIGS. 26A and 26B are graphs showing examples of a slant SPG wavelengthspectrum when the slant angle is changed.

FIG. 27 is a graph showing an example of a wavelength spectrum of aconventional slant SPG.

FIG. 28 is a graph showing an example of a wavelength spectrum of aslant SPG in which a side band and a main band are present.

BEST MODE FOR CARRYING OUT THE INVENTION 1. First Embodiment

The present inventors firstly conducted research aimed at achieving anarrow loss band.

A detailed description of the present invention will now be givenfollowing the research process of the present invention.

In the first embodiment, under conditions that can be applied to a slantSPG whose grating period is essentially fixed, the effects of “narrowloss band” and “side band loss peak suppression” are obtained.

As described above, in a slant SPG it is possible in some cases to makedivisions into main bands, which are wavelength regions where a largeloss peak is obtained in the transmitted light wavelength spectrum, andside bands, which are small wavelength regions that appear on the shortwavelength side of the main bands.

FIG. 28 shows an example of a wavelength spectrum in which a main bandand a side band are present. The long wavelength side is the main band,and the short wavelength side is the side band.

There are cases in an optical filter when transmission loss in the sideband becomes noise, as is described above.

Moreover, the smaller loss ratio between transmission losses of the mainband and the side band in the optical filter, the greater the degree offreedom in design. Therefore, a smaller loss ratio is preferable.

Accordingly, “side band loss peak suppression” is sought.

FIG. 1 shows design conditions of three parameters that are the diametera of a core, a standardized frequency V, and a relative photosensitivityratio P of a core relative to a photosensitive layer adjacent to thecore in the clad.

As is shown in FIG. 1, the clad is formed by a first layer C adjacent tothe core, and a second layer D on the outer periphery thereof. The firstlayer C is a photosensitive layer formed from quartz glass to which aphotosensitive dopant has been doped.

In this example, the radius of the first layer C is 5 times the coreradius a/2. The radius of the clad is 62.5 μm.

In these design conditions a description is given of what kind of effectthe aforementioned three parameters have on the frequency band of themain band, and on the ratio of side band loss to main band loss.

In the graph, the refractive index profile of the optical fiber isenclosed by a solid line.

In the refractive index profile, the core is set to have the highestrefractive index, while the first layer of clad C and the second layerof clad D are set the same. Note that it is not absolutely necessary forthe refractive indexes of the first layer C and the second layer D tomatch, and cases such as the refractive index of the first layer C beinghigher, or conversely, the refractive index of the second layer D beingset higher may also be considered.

The photosensitivity profile is expressed with the relativephotosensitivity ratio shown on the vertical axis as a reference, and isenclosed by a dot—dash chain line.

In this profile the greatest amount of photosensitive dopant is doped tothe first layer C.

The relative photosensitivity ratio is the ratio of the amount ofphotosensitive dopant doped to other layers (i.e., other layers formingthe core or the clad; in this example, the core and the second layer D)when the concentration of photosensitive dopant in the photosensitivelayer to which the greatest amount of photosensitive dopant has beendoped (in this example, the first layer C) is taken as 1.

Note that it is not necessary for the concentration of photosensitivedopant to be constant inside the core. If there are varying amounts ofconcentration of photosensitive dopant inside the core, the relativephotosensitivity ratio is calculated from the average dopantconcentration inside the whole core.

As can be understood from FIG. 1, in this embodiment a small amount ofphotosensitive dopant is doped to the core, and no photosensitive dopantis doped to the second layer D.

In the conventional example, an example is shown in which photosensitivedopant is doped only to the core, however, in this embodimentphotosensitive dopant is doped mainly to the first layer of clad C,while a small amount of photosensitive dopant is further doped to thecore.

Germanium is doped to the core in order to adjust the relativephotosensitivity ratio, while phosphorous, aluminum, and the like aredoped in order to adjust the refractive index.

Phosphorous and aluminum are dopants that have no photosensitivity andalso act to raise the refractive index.

Germanium is doped to the first layer of clad C in order to adjust thephotosensitivity thereof, while boron, fluorine, and the like may bedoped if necessary in order to adjust the refractive index thereof.

The second layer D is formed from pure quartz glass or from quartz glassto which boron, fluorine, or the like has been doped in order to adjustthe refractive index thereof.

In this embodiment, the diameters of the three cores examined were 7, 8,and 10 μm.

The standardized frequency V is determined by the following formulausing the diameter of the core and the comparative refractive indexdifference between the core and the clad: $\begin{matrix}{V = {\frac{2\quad \pi}{\lambda} \cdot \frac{a}{2} \cdot n_{core} \cdot \sqrt{2\quad \Delta}}} \\{\Delta = \frac{n_{core}^{2} - n_{clad}^{2}}{2\quad n_{core}^{2}}}\end{matrix}$

In the formula: λ is the operating wavelength; a is the diameter of thecore in units of μm; n_(clad) is the refractive index of the clad;n_(core) is the refractive index of the core, and Δ is the comparativerefractive index difference between the refractive index of the clad andthe refractive index of the core. The standardized frequency V varieswithin a range between 1.7 and 2.3.

The relative photosensitivity ratio of the core varies within a rangebetween 0 to 0.4.

Note that, in the present embodiment the operating wavelength of theslant SPG is 1,500 to 1,600 nm.

Firstly, after values are set for the diameter of the core, thestandardized frequency, and the relative photosensitivity ratio of thecore, the slant angle is set to the first angle (reflection suppressionangle) at which the loss caused by the coupling of the waveguide modewith the reflection mode (reverse LP01 mode) reaches the minimum value(normally approximately 0 to 0.01 dB) when the slant angle is graduallymade larger starting from 0 degrees. Accordingly, in the presentembodiment there is almost no coupling with the reflection mode. Theslant angle may differ due to other conditions; however, the slant angleis between 1.5 and 8 degrees, and preferably between 1.5 and 6 degrees.

Next, the effective refractive index and the coupling coefficient arecalculated for the coupling of the waveguide mode with an LP0X modegroup and the coupling of the waveguide mode with an LP1X mode group.The LP0X mode group and the LP1X mode group are clad mode groups thatform main bands and side bands.

These effective refractive index and coupling coefficient are thenconverted into the coupled wavelength (the wavelength when the waveguidemode is coupled with the clad mode) and transmission loss obtained whenthe slant SPG is made with an operating wavelength of 1,550 nm and afixed grating period by using mode coupling theory to find the sum ofthe transmission loss generated by each coupling.

FIG. 2 is a graph showing an example of a calculation result. The symbol represents points when the wavelength (coupled wavelength) obtained bycoupling the LP0X mode (LP01, LP02 . . . ) and the waveguide mode andthe transmission loss at this time are plotted. The symbol ◯ representspoints when the wavelength (coupled wavelength) obtained by coupling theLP1X mode (LP11, LP12 . . . ) (X is an integer) and the waveguide modeand the transmission loss at this time are plotted.

The loss frequency band of the main band (i.e., the main band frequencyband) is the width from the coupled wavelength of the LP11 modeappearing on the longest wavelength side of the main band to the coupledwavelength of the first LP1X mode in which the loss is at the minimum.

FIGS. 3A to 5B show results obtained when the main band frequency bandand the side band/main band loss are determined by performingcalculations under various conditions that are set by changing thediameter a of the core, the standardized frequency V, and the relativephotosensitivity ratio P of the core, and, in the same way, bydetermining the slant angle (reflection suppression angle) when thecoupling with the reflection mode is at the minimum.

FIGS. 3A and 3B are graphs showing a relationship between a relativephotosensitivity ratio of a core and a main band frequency band when thediameter of the core is 7 μm, and a relationship between a relativephotosensitivity ratio of the core and a side band/main band loss ratiowhen the diameter of the core is 7 μm.

The results are grouped for each standardized frequency.

FIGS. 4A and 4B are graphs showing the same relationships when thediameter of the core is 8 μm.

FIGS. 5A and 5B are graphs showing the same relationships when thediameter of the core is 10 μm.

Note that the main band loss is the top value of the peak of the mainband transmission loss, and the side band loss is the top value of thepeak of the side band transmission loss.

It can be seen from these graphs that the main band frequency bandincreases as the relative photosensitivity ratio of the core increases.

Namely, because the amount of change in the refractive index increasesas the relative photosensitivity ratio of the core increases, couplingwith the reflection mode tends to occur easily. Accordingly, in order toprevent this, it is necessary to increase the slant angle. In addition,because there is a tendency for the main band frequency band to increaseas the slant angle increases, the result of this is that there is alarge main band frequency band.

The main band frequency band also depends to a comparatively largeextent on the diameter of the core and the standardized frequency. Thereis a tendency for the main band frequency band to become narrower as thediameter of the core increases, and to become narrower as thestandardized frequency V becomes smaller.

Namely, there is a tendency for light to spread out over the crosssection of the fiber as the diameter of the core increases. Moreover, ifthe standardized frequency becomes smaller while the diameter of thecore remains the same, the core-clad comparative refractive indexdifference becomes smaller and, in the same way, there is a tendency forthe light to spread out.

In a slant SPG there is also a dependency of the periodic structure onthe direction of the fiber cross section, however, the phase matchingconditions in the direction of the cross section are also constrained bythe spreading out of the light. As a result, coupling with thereflection mode is reduced even when the slant angle is small, and it ispossible to narrow the main band.

Moreover, the side band/main band loss ratio becomes smaller as therelative photosensitivity ratio of the core increases. The reason forthis is given below.

FIG. 6 shows the electric field strength of a clad mode forming a sideband. The electric field strength of the waveguide mode is also shown.

On the clad side in the vicinity of the boundary between the core andthe clad, the waveguide mode has a comparatively strong positiveelectric field strength, while the clad mode within the side band has anegative electric field strength and is in the opposite direction.Accordingly, the coupling coefficient is a negative value. In contrast,on the core side, the waveguide mode and the clad mode have the samepositive electric field strength, and are in the same direction. Theoverlap between these two modes has a positive value on the core side.Accordingly, if a grating is formed in the core, then the overlap isoffset by the core side and the clad side, and the coupling coefficientis reduced.

The side band/main band loss ratio is not particularly dependent on thediameter of the core and the standardized frequency, and there is atendency for the side band/main band loss ratio to become greatlyreduced whatever the conditions if the relative photosensitivity ratioof the core is in the vicinity of 0.2.

On the basis of these premises, slant SPG conditions that are actuallyfeasible and that the objects of the present invention to be achievedare a main band frequency band of 10 nm or less, and a side band/mainband loss ratio of 0.2 or less. It is naturally to be understood thatconventionally these slant SPG conditions have not been achieved. Byproviding a slant SPG with properties such as these the effect isobtained that the degree of freedom in design when manufacturing anoptical filter is increased. In addition, when applied to a gainequalizer (abbreviated below to GEQ) that flattens (i.e., equalizes)gain in an erbium doped optical fiber amplifier (abbreviated below toEDFA), the effect is obtained that the gain equalization residue can bereduced.

Furthermore, when trying to determine a range that satisfies this rangefrom the relationship between the diameter of the core, the relativephotosensitivity ratio of the core, and the standardized frequency, therange shown in FIG. 7 may be proposed.

Note that, in this calculation example, a range of 7 μm or greater issought, however, essentially, this range is one in which the diameter ofthe core is 5 μm or more and in which the above Formula (1) issatisfied.

FIG. 8 shows an example of a wavelength spectrum of transmitted light ofa slant SPG produced under conditions such as these.

It can be seen that preferable characteristics are obtained, namely, themain band frequency band is a narrow 8.5 nm, and the side band/main bandloss ratio is a small 0.18.

In this slant SPG, the core is formed from quartz glass to whichgermanium and aluminum have been doped, the first layer C of clad isformed from quartz glass to which germanium and fluorine have beendoped, and the second layer D of clad is formed from quartz glass towhich fluorine has been doped.

The relative photosensitivity ratio of the core is 0.18, and thestandardized frequency is 2.3. In addition, the diameter of the core is10 μm, the core-clad comparative refractive index difference is 0.3%,the outer diameter of the photosensitive layer of the clad is 40 μm, theclad diameter is 125 μm, the mode field diameter is 12 μm, the Braggwavelength is 1,550 nm, the grating period is 536 nm, the grating length(i.e., the length of the grating portion) is 10 mm, the slant angle is 3degrees, and the bend loss of a roll diameter of 60 mm is 0.02 dB.

The conditions for the slant SPG of the present embodiment are a corediameter of 5 μm or more, and preferably of 7 μm or more, and that theabove Formula (1) is satisfied, however, it is also desirable that thecondition below is satisfied.

Namely, it is preferable that the relative photosensitivity ratio of thecore is between 0.1 to 0.4. If the relative photosensitivity ratio ofthe core is outside this range, then it may not be possible, in somecases, to obtain the desired characteristics.

Moreover, it is also desirable from the viewpoint of enabling asufficient transmission loss to be obtained that the outer diameter ofthe photosensitive layer of the clad is 4 times or more the diameter aof the core.

It is also preferable that the diameter of the core is 12 μm or less. Ifthe diameter of the core exceeds 12 μm, then problems are caused by thebend loss being too great. Moreover, the desired characteristics may notbe able to be obtained.

Furthermore, in the range shown in FIG. 7, the core-clad comparativerefractive index difference is 0.5% or less. Essentially, it isdesirable that it be between 0.2 and 0.4%. If it exceeds 0.5%, thedesired characteristics may not be able to be obtained.

It is also desirable that, in the operating wavelength, preferably in awavelength of 1,550 nm, the bend loss of the optical fiber forming thegrating is I dB/m or less at a roll diameter of 60 mm. More preferableis a bend loss in conditions of a wavelength of 1,550 nm and a rolldiameter of 40 mm of 0.1 dB/m or less, most preferable of 0.01 dB/m orless.

If the bend loss is too large, then problems occur such as the ease ofhandling deteriorating when the optical fiber is housed in a module.

Furthermore, it is preferable that the mode field diameter of thewaveguide mode in the operating wavelength (in the present embodiment1500 to 1600 nm and preferably 1500 nm) of the optical fiber used in theslant SPG is 15 μm or less. If it exceeds 15 μm the light confinement isweak and the loss is high, leading to cases where it is not suitable foractual use. There is also the concern that there will be a largeconnection loss if the optical fiber is connected to another opticalfiber.

The bend loss and the mode field diameter are greatly affected by thediameter of the core. The larger the diameter of the core, the greaterthe bend loss. Moreover, the mode field diameter also becomes larger.Therefore, it is desirable that the diameter of the core is 12 μm orless, as is described above.

In the slant SPG of the present embodiment the grating period isapproximately one third to one half the operating wavelength and are setdepending on the desired characteristics. However, in order to obtain anarrow main band frequency band, it is desirable that the grating periodis a fixed period. Moreover, if the grating period is a fixed period, itis desirable that the grating length is short. If the grating period istoo long, the spectrum coupled with each clad mode is too narrow, andthere is a tendency for the ripples to become larger. There are noparticular limits, however, the grating length is preferably between 1and 100 mm or less, and more preferably 5 mm or less.

If the grating length is less than 1 mm, the concern arises that thegrating length will be too short and the required transmission loss willnot be able to be obtained. If the grating length exceeds 100 mm, theconcern arises that not only will formation of the grating portion bedifficult, but also that the device will be too large which will causeproblems when the device is housed in a module or the like.

Because the grating length has an effect on the optical characteristicssuch as the filter frequency band, the transmission loss, and the like,it is preferable that the grating length is suitably adjusted whileconsidering the desired characteristics.

It is also preferable that the outer diameter of the photosensitivelayer of the clad is 1.5 times or more the mode field diameter of thewaveguide mode of the operating wavelength (1,500 nm to 1,600 nm in thepresent embodiment and preferably 1,500 nm) of this slant SPG. There isno particular restriction as to the upper limit value; however, it ispractically set at 8 times or less.

If the above value is less than 1.5 times, because the grating portionof the photosensitive layer is not formed in the area where thewaveguide mode is propagated, there are times when sufficient loss peakscannot be obtained.

Once these conditions have been satisfied it is desirable that the outerdiameter of the photosensitive layer of the clad is 60 μm or less.

Because there is a tendency for the photosensitive layer to absorb lightof a specific wavelength that is irradiated thereon during formation ofthe grating, if the outer diameter of the photosensitive layer is toolarge, when light is irradiated from the side surface of the opticalfiber, the necessary and sufficient light is not irradiated onto theportion of the photosensitive layer located on the opposite side to thelight irradiation surface. As a result of this, it is not possible forthe refractive index to be raised sufficiently and, in some cases, thechange in the refractive index is not uniform.

Providing the clad is provided with a photosensitive layer, this may beone layer or may be a multilayered structure formed from two or morelayers, however, from the viewpoint of manufacturability a multilayeredstructure of two or more layers is preferable.

Furthermore, it is possible to alter as is appropriate conditions suchas the doping amounts of photosensitive dopant and dopant for adjustingthe refractive index in accordance with the design conditions.

Moreover, in the present embodiment it is possible to manufacture theoptical fiber used in the slant SPG by a known method such as the VADmethod, the MCVD method, the PCVD method, or the like. The gratingportion may be manufactured by a known method using an excimer laser orthe like as the light source.

In this way, in the slant SPG of the present embodiment, because themain band frequency band is narrow and the side band loss is small inthe transmitted light wavelength spectrum, a loss peak is obtained in anarrow frequency band.

Note that it is possible to reliably manufacture a slant SPG having thedesired characteristics if the slant SPG is designed and manufactured inaccordance with the above described procedure.

2. Second Embodiment

The first embodiment is preferably applied when the grating period is afixed period, however, there are cases when it is not always possible toachieve a satisfactory effect when it is applied to a chirped pitch inwhich the grating period changes. In order to enlarge the degree offreedom in the design conditions, for example, after a narrow lossfrequency band has been set, it is preferable for it to be possible tofurther apply the present invention to a chirped pitch and make furtherfine adjustments.

The second embodiment is able to be applied without any distinctionbeing made between when the grating period is a fixed period and whenthere is a chirped pitch.

2-1. Conditions for Obtaining a Narrow Loss Frequency Band:

Firstly, the present inventors investigated conditions that would enablea main band frequency band to be narrowed.

As is described above, if the main band frequency band is narrow and theside band loss is comparatively small, then it is possible to narrow theloss frequency band.

In the present embodiment as well, slant SPGS were manufactured under avariety of conditions using an optical fiber having the structure shownin FIG. 1. The characteristics of these were then compared.

Note that the grating period of the slant SPG of the present embodimentalso depends on conditions such as the operating wavelength and thelike, however, the grating period may be set, for example, toapproximately one third to one half the operating wavelength. In thecase of a chirped grating, it is sufficient if the chirping ratio isgreater than 0 and the chirping ratio may be set, for example, to 20nm/cm or less, and preferably to 0.2 to 10 nm/cm. The chirping ratioshows the ratio of the changed grating period in the longitudinaldirection of the optical fiber. In particular, when the chirping ratiois 20 nm/cm or less, then at a grating length of approximately 7 mm itis possible to satisfactorily cover the 40 nm band, which is thefrequency band normally required for gain equalization in order toequalize the gain of a C-Band or Er doped optical fiber amplifier.

Note also that a chirped pitch is one whose grating period is graduallychanged so as to become extended or contracted in the longitudinaldirection of the optical fiber. For example, provided that the followingare known; namely, the grating length, the grating period which is thereference for the grating period in the center in the longitudinaldirection of the grating portion and the like, the chirping ratio, andwhether or not the grating period is gradually extended or contracted,then it is possible to specify the layout state of the high refractiveindex portion of the grating portion.

In the present embodiment, under the design conditions shown in FIG. 1,the radius of the outer diameter of the first layer C used in theinvestigation is 15 μm and the radius of the clad is 62.5 μm.

Furthermore, both the first layer C and the second layer D are formedfrom quartz glass. Germanium is doped to the core and to the first layerC, and the present embodiment is the same as the first embodiment inthat other dopants may also be doped to each layer if required.

Note that, in the first embodiment, it is essential that aphotosensitive dopant is doped to the core, however, in the secondembodiment, provided that the conditions of Formula (2) are satisfied asis described below, then there are cases in which a photosensitivedopant may not be doped to the core.

Moreover, in the first embodiment, it is necessary that thephotosensitive layer of the clad be adjacent to the core, however, inthe second embodiment, it is not essential that it be adjacent to thecore, and, in the graph shown in FIG. 1, it is possible, for example,for the second layer D to be made the photosensitive layer, or to formthe clad with three or more layers and to make a central layer thereofthe photosensitive layer.

In the present embodiment, the effects of the three parameters givenbelow on the optical characteristics were investigated. Namely,

{circle around (1)} the diameter a of the core

{circle around (2)} the standardized frequency V, and

{circle around (3)} the relative photosensitivity ratio P of the core tothe photosensitive layer of the clad.

The details of these investigations are described below.

Note that, in the second embodiment, the relative photosensitivity ratioP of the core is the relative photosensitivity ratio of the core to thatphotosensitive layer of the clad that has the highest photosensitivity.

Namely, in the second embodiment, it is possible to provide the cladwith two or more photosensitive layers. The relative photosensitivityratio of the core represents the relative ratio to that photosensitivelayer that has the highest photosensitivity (i.e., whose concentrationof doped photosensitive dopant is the highest) from among thephotosensitive layers.

The various numerical ranges investigated were as follows:

{circle around (1)} the diameter a of the core: 4 to 10 μm

{circle around (2)} the standardized frequency V: 1.7 to 2.3

{circle around (3)} the relative photosensitivity ratio P of the core tothe photosensitive layer of the clad: 0 to 0.3

Note that, in the present embodiment, the operating wavelength of theslant SPG is 1,550 nm.

Moreover, in all of the calculation conditions the amount of change inthe refractive index of the high refractive index portion 3 of thegrating portion 4 shown in FIG. 24 is 0.001, while the grating length(i.e., the length of the grating portion 4) is 1 mm.

Firstly, combinations of the three values of {circle around (2)} thediameter a of the core, {circle around (1)} the standardized frequencyV, and {circle around (3)} the relative photosensitivity ratio P of thecore to the photosensitive layer of the clad are set. For each of theseset conditions, the slant angle θ is gradually increased from zerodegrees, and the first angle (i.e., the reflection suppression angle) atwhich the transmission loss caused by coupling with the reflection mode(reverse LP01 mode) reaches the minimum value (normally, approximately 0to 0.01 dB) is taken as the slant angle θ. The slant angle θ differs dueto other conditions as well, however, essentially, it is between 1.5 and8 degrees, and preferably between 1.6 and 6 degrees.

Next, effective refractive index and coupling constant calculations areperformed for a coupling of a waveguide mode with the LP0X mode groupand LP1X mode group for a slant SPG in which the combinations of thethree values of {circle around (1)} the diameter a of the core, {circlearound (2)} the standardized frequency V, and {circle around (3)} therelative photosensitivity ratio P of the core to the photosensitivelayer of the clad and the slant angle are fixed as the reflectionsuppression angle.

As described above, the couplings with the LP0X mode groups and the LP1Xmode groups are couplings with clad mode groups that form a main bandand side bands.

FIG. 9 is a graph showing an example of a result of this calculation.The symbol  represents the LPOX mode (LP01, LP02 . . . ), and thesymbol ◯ represents the LP0X mode (LP01, LP02 . . . ) (wherein X is aninteger).

Note that the main band loss frequency band (the main band frequencyband) is taken between the LP11 mode that appears on the longestwavelength side of the main band and the coupling wavelength thatcorresponds to the first LP1X mode where the loss is at the minimum. Inaddition, the frequency band on the shorter wave side of this where acoupling occurs is taken as the side band loss frequency band (side bandfrequency band).

Furthermore, this effective refractive index and coupling coefficientare then converted into the coupled wavelength and transmission lossobtained when a transmission loss is created for a slant SPG underconditions of a center grating period of 530 nm and a chirping ratio of0.35 nm/mm, and that has a form in which the grating period is graduallyenlarged, by determining the transmission loss in each mode usingtransmission queues so as to calculate the sum of the transmissionlosses thereof. Thereafter, a graph showing the relationship betweenwavelength and transmission loss, such as that shown in FIG. 10, isobtained. The main band frequency band is determined from this graph.

This calculation was performed for each slant SPG in which thecombination of the three values of {circle around (1)} the diameter a ofthe core, {circle around (2)} the standardized frequency V, and {circlearound (3)} the relative photosensitivity ratio P of the core to thephotosensitive layer of the clad is changed, and the respective mainband frequency bands (nm) thereof were determined.

FIGS. 11A, 11B, 12A, and 12B are graphs showing the relationship betweenthe relative photosensitivity ratio P and the main band frequency bandfor the respective standardized frequencies V.

In each graph are shown the respective graph lines for each of the corediameters a.

From these graphs it can be seen that in a chirped pitch slant SPG themain band frequency band becomes larger as the relative photosensitivityratio of the core becomes larger, and also that this trend becomes moreremarkably the smaller the radius of the core.

The larger the relative photosensitivity ratio of the core, the largerthe amount of change in the refractive index of the core when thegrating section is being formed. Therefore, coupling with a reflectionmode occurs more easily. Thus, in order to prevent such coupling with areflection mode it becomes necessary to increase the size of the slantangle θ.

In contrast, because there is a tendency for the main band frequencyband to become larger as the slant angle θ becomes larger, the result isthat the main band frequency band becomes larger.

Moreover, from these graphs it can be confirmed that the main bandfrequency band also depends on the diameter of the core and thestandardized frequency. Namely, there is a tendency for the main band tobecome narrower as the diameter of the core increases, and to becomenarrower as the standardized frequency becomes smaller. Namely, there isa tendency for light to spread out over the cross section of the opticalfiber as the diameter of the core increases. Moreover, if thestandardized frequency becomes smaller while the diameter of the coreremains the same, the core-clad comparative refractive index differencebecomes smaller and, in the same way, there is a tendency for the lightto spread out.

In a slant SPG there is also a dependency of the periodic structure onthe direction of the fiber cross section, however, the phase matchingconditions in the direction of the cross section are also constrained bythe spreading out of the light. As a result, coupling with thereflection mode is reduced even when the slant angle θ is small, and itis possible to narrow the main band frequency band.

Accordingly, it is clear from the graphs shown in FIGS. 11A to 12B thatin order to narrow the main band frequency band, it is sufficient if therelative photosensitivity ratio of the core is made smaller, thediameter of the core is made larger, and the standardized frequency ismade smaller.

Here, the main band frequency band of a slant SPG that is actuallypracticable and that the objects of the present invention to be achievedis taken as 10 nm or less. A relationship between {circle around (1)}the diameter a of the core, {circle around (2)} the standardizedfrequency V, and {circle around (3)} the relative photosensitivity ratioP of the core to the photosensitive layer of the clad that satisfies thecondition of a main band frequency band of 10 nm or less is representedby Formula (2).

If the diameter of the core, the standardized frequency, and therelative photosensitivity ratio of the core are set so as to satisfythis relationship, then if the grating period is constant, a slant SPGcan be obtained whose main band frequency band has narrow transmissioncharacteristics regardless of whether or not a chirped pitch isemployed.

Note that, in Formula (2), if the numerical range of the relativephotosensitivity ratio P is 0 or less, or is an imaginary number, then astructure is employed in which the relative photosensitivity ratio P isset at zero and a photosensitive dopant is not doped to the core.

By satisfying Formula (2) the effect is obtained that the degree offreedom in design when creating an optical filter is increased. Inaddition, when applied to a gain equalizer that equalizes gain in anerbium doped optical fiber amplifier, the effect is obtained that thegain equalization residue can be reduced.

2-2. Conditions for Enlarging Transmission Loss (Main Band Area):

In accordance with the type of application there may be a need for anoptical filter to not only be able to narrow the loss band, but to morepreferably be able to “enlarge transmission loss (main band area)”. Thisis because in order to efficiently filter light of a specific wavelengthit is necessary to increase the power of light from the waveguide modecoupling with the clad mode.

The power of this coupling light increases if the amount of change inthe refractive index of the grating section is increased. However, thereis a limit to the increase in the amount of change in the refractiveindex. For example, the amount of change in the refractive index is1.0×10⁻² or less, and essentially is between 5.0×10⁻⁴ and 5.0×10⁻³.

Therefore, characteristics are sought whereby the power of lightcoupling with the clad mode is increased sufficiently even by a smallamount of change in the refractive index.

Note that here a small amount of change in the refractive index is, forexample, 3×10⁻³ or less, and preferably is between 5.0×10⁻⁴ and2.0×10⁻³.

Therefore, investigations were carried out for conditions in which theintegral value of the loss peak of the main band shown in FIG. 10increased. The integral value is the surface area of the diagonal lineportion of the graph shown in FIG. 10.

Namely, as was explained in 2-1 above, graphs were sought that show awavelength-transmission loss relationship such as that shown in FIG. 10,and the integral values of the loss peaks of the main bands of thesegraphs were then determined.

This calculation was performed for each slant SPG that was obtained bytaking the slant angle as the reflection suppression angle and thenchanging the combination of the three values of {circle around (1)} thediameter a of the core, {circle around (2)} the standardized frequencyV, and {circle around (3)} the relative photosensitivity ratio P of thecore to the photosensitive layer of the clad. The integral values of thearea of the loss peak of the main band were then each determined bynumerical calculation. The units for the integral values are dB·nm. Notethat the integral values used here are not absolute values but arerelative values used for comparing the size of the transmission lossarea when the parameters are changed.

In this calculation example, the integral value was set as 12.08, when:

the standardized frequency V=1.9,

the core diameter a=8 μm, and

the core relative photosensitivity ratio P=0 and was set as a reference.

FIGS. 13A, 13B, 14A, and 14B are graphs showing the relationship betweenthe relative photosensitivity ratio P and the integral value of the mainband transmission loss area for the respective standardized frequenciesV. In each graph are shown the respective graph lines for each value ofthe core diameters a.

From these graphs it can be seen that there is a tendency for theintegral value to be bigger the larger the relative photosensitivityratio. This is because the coupling efficiency with the clad modeincreases as the relative photosensitivity ratio of the core increases.

The integral value also depends on the standardized frequency, andincreases as the standardized frequency is reduced. This is because thesmaller the standardized frequency, the easier it is for more waveguidemode to leak into the photosensitive layer of the clad having the largerphotosensitive ratio.

Note that if the standardized frequency is the same, it is also possibleto confirm that there is almost no effect from the diameter of the coreon the integral value.

Accordingly, it is clear that, in order to increase the integral value,it is sufficient to increase the relative photosensitivity ratio of thecore and to decrease the standardized frequency.

Here, in consideration of achieving the aim of obtaining opticalcharacteristics that are actually practicable and in which there is alarge transmission loss, the integral value of the slant SPG was set as15 or more.

By satisfying these conditions the following effects are achieved.Namely, because it is possible to achieve a large loss with the samechange in the refractive index, when making optical filters with thesame loss, these can be made with a short exposure time. Moreover, if achange in the refractive index can be brought about while irradiatingthe light for the same length of time, then an optical filter can beproduced having greater transmission loss. Moreover, if the presentinvention is applied, for example, to a gain equalizer that equalizesthe gain of an erbium doped optical fiber amplifier, then a massproduction effect is obtained through the reduction in the exposuretime. Note that because a larger integral value is more preferable thereis no particular limit on the maximum value.

In order to satisfy these conditions, it is preferable that the relativephotosensitivity ratio of the core satisfies Formula (3).

Note that, in Formula (3), if the numerical range of the relativephotosensitivity ratio P is 0 or less, or is an imaginary number, then astructure is employed in which the relative photosensitivity ratio isset at zero and a photosensitive dopant is not doped to the core.

Moreover, it is preferable if both Formula (2) and Formula (3) aresatisfied, as this enables the main band frequency band to be narrowedand the transmission loss to be increased.

FIG. 15A shows the wavelength spectrum of a slant SPG produced under thefollowing conditions which does not satisfy both Formula (2) and Formula(3).

the relative photosensitivity ratio P=0.2

the standardized frequency V=2.3

the core diameter a=5 μm.

FIG. 15B shows the wavelength spectrum of a slant SPG produced under thefollowing conditions which does satisfy both Formula (2) and Formula(3).

the relative photosensitivity ratio P=0.1

the standardized frequency V=1.7

the core diameter a=5 μm.

In the wavelength spectrum shown in FIG. 15A, there is no differencebetween the main band and side band, and the entire loss peak forms asubstantially single peak over a wide frequency band. The frequency bandof this peak is 29 nm, while the integral value of the main band isapproximately 13, which is small.

In contrast to this, in the wavelength spectrum shown in FIG. 15B, themain band is sufficiently large relative to the side band. In addition,the main band frequency band is 6.5, which is sufficiently narrow, whilethe integral value of the loss peak of the main band is 19, which issufficiently large.

2-3. Conditions for Suppressing Ghost Mode Peaks:

In accordance with the type of application it may be more preferable ifthere is a need for “suppressing ghost mode peaks”.

FIG. 16 shows an example of a wavelength spectrum of transmitted lightin which a ghost mode peaks is present. A ghost mode is a clad mode,from among the clad modes that couple with the waveguide mode, thatcouples to a particularly large extent on the long wave side with awaveguide mode.

As is shown in FIG. 16, if this ghost mode peak is present then it isnot possible to obtain filter characteristics that have a smooth longwavelength side.

A ghost mode peak is generated when the ratio of waveguide modecouplings with the LP11 mode, which is a lower order clad mode, is toogreat relative to the couplings of the waveguide mode with other modes.

In the same way as the examples shown in 2-1 and 2-2 above, FIGS. 17A,17B, 18A, and 18B are diagrams in which, under the design conditionsshown in FIG. 1, in a chirped pitch slant SPG in which a reflectionsuppression angle has been set, the ratios (i.e., the coupling constantratios) of the coupling constants with the LP11 mode relative to thelargest coupling constants from among the coupling constants with theother modes are shown in graphs in their relationships with thestandardized frequencies.

In each of these graphs the core diameter a is constant.

Moreover, each graph shows the respective core relative photosensitivityratios P.

Note that the smaller the coupling constant the more difficult it is forghost mode peaks to be generated.

From these graphs it can be seen that the coupling constant ratio isalso greatly dependent on the standardized frequency, and that thelarger the standardized frequency the smaller the coupling constantratio and the easier it is for ghost mode peaks to be generated. This isbecause the larger the standardized frequency the stronger the electricfield distribution of the LP11 mode is in the vicinity of the core, andthere is increased overlapping of the electric field distribution of theLP11 mode with the electric field distribution of the waveguide mode.

FIG. 19A is a graph showing the electric field distributions of the LP11mode and waveguide mode when the core diameter a is 8 μm and thestandardized frequency is 1.7. FIG. 19B is a graph showing the electricfield distributions of the LP11 mode and waveguide mode when the corediameter a is 8 μm and the standardized frequency is 2.3.

Here, the coupling constant ratio is regulated to 0.2 or less as a rangethat does not allow the ghost mode peaks to become a problem.

By satisfying these conditions an optical filter whose long wavelengthside also had smooth characteristics was obtained. Moreover, an opticalfilter with a narrower filter frequency band and whose long wavelengthside also had smooth characteristics when applied to a gain equalizerthat equalizes gain in an Er doped optical fiber amplifier was obtained.

In order to satisfy these conditions it is preferable that the relativephotosensitivity ratio of the core satisfies Formula (4).

Note that, in Formula (4), if the numerical range of the relativephotosensitivity ratio P is 0 or less, or is an imaginary number, then astructure is employed in which the relative photosensitivity ratio isset at zero and a photosensitive dopant is not doped to the core.

FIG. 20A shows an example of the wavelength spectrum of a slant SPGproduced under the following conditions which does not satisfy Formula(4).

the standardized frequency V=2.3

the core diameter a=7 μm.

the core relative photosensitivity ratio P=0.15

FIG. 20B shows an example of the wavelength spectrum of a slant SPGproduced under the following conditions which does satisfy Formula (4).

the standardized frequency V=1.7

the core diameter a=7 μm.

the relative photosensitivity ratio P=0.1

If these graphs are compared it becomes clear that by satisfying Formula(4) ghost mode peaks are reduced.

Note that in the second embodiment, it is sufficient if one or more ofthe three conditions shown in the above 2-1 to 2-3 are satisfied, andpreferable if two conditions are satisfied, and most preferable if allthree conditions are satisfied.

2-4. Conditions for Suppressing Side Band Mode Loss Peaks:

As was described in the first embodiment above, the smaller thedifference between transmission losses of the main band and the sideband in the optical filter, the greater the degree of freedom in design.Therefore, a smaller difference is preferable.

Accordingly, “suppression of side band loss peaks” is sought.

Here, in the first embodiment, the conditions were for applying when thegrating period was constant, however, in the present embodiment, theconditions can be applied regardless of whether the grating period isconstant or whether there is a chirped pitch.

In the same way as for 2-1 to 2-3 above, FIGS. 21A, 21B, 22A, and 22Bare graphs in which, in a chirped pitch slant SPG in which a reflectionsuppression angle has been set, relationships between the core diametera and the transmission loss ratio represented as dB of the side bandrelative to the main band (i.e., the side band/main band loss ratio) areshown.

In each of these graphs the standardized frequency V is constant.

Moreover, each graph shows the respective core relative photosensitivityratios P.

From these graphs it can be understood that the side band/main band lossratio has substantially no dependency on the standardized frequency andthe core diameter, and is only affected by the relative photosensitivityratio of the core.

Furthermore, as was explained using the graph shown in FIG. 6 for thefirst embodiment, in order to reduce the side band/main band loss ratioit is preferable that there is a large core relative photosensitivityratio.

In order to make the side band/main band loss ratio 0.1 or less, it isnecessary to set the core relative photosensitivity ratio to 0.2 ormore.

By providing characteristics such as these, the effect is obtained thatthe degree of freedom in design when creating wider frequency bandfilter characteristics is increased. In addition, when applied to a gainequalizer that equalizes gain in an Er doped optical fiber amplifier,the effect is obtained that the gain equalization residue can be reducedover a wide frequency band.

FIG. 23A shows an example of the wavelength spectrum of a slant SPGproduced under the following conditions.

the standardized frequency V=1.7

the core diameter a=7 μm.

the core relative photosensitivity ratio P=0.00

FIG. 23B shows an example of the wavelength spectrum of a slant SPGproduced under the following conditions.

the standardized frequency V=1.7

the core diameter a=7 μm.

the relative photosensitivity ratio P=0.25

From these graphs it is clear that the side band can be suppressed bysetting the core relative photosensitivity ratio to 0.2 or more. Notethat these conditions should be satisfied after satisfying at least onefrom the above Formulas (2) to (4).

2-5. Concerning Other Optical Characteristics:

In the present embodiment, it is desirable that, in the 1,550 nmwavelength, bend loss of the optical fiber used in the slant SPG is notmore than 1 dB/m at a winding diameter of 60 mm. It is more preferablethat the bend loss be not more than 0.1 dB/m, and even more preferably0.01 dB/m or less, at a winding diameter of 40 mm. The greater the bendloss the more the ease of handling and the like is reduced when housedin a module. Therefore, this is disadvantageous.

Further, it is preferable that the mode field diameter in the operatingwavelength of the optical fiber (for example, 1500 to 1600 nm, andpreferably 1550 nm) is 15 μm or less. If the mode field diameter exceeds15 μm, the light confinement is weakened and the loss increases, whichmay render the apparatus unsuitable for practical application. Thepossibility of increased connection loss when the optical fiber isconnected to another optical fiber also exists.

Note that the bend loss and mode field diameter are greatly affected bythe core diameter a, and the bending loss increases if the core diametera is increased. The mode field diameter also increases. Therefore, it ispreferable that the core diameter a is, for example, 12 μm or less.

It is also preferable that the outer diameter of the photosensitivelayer of the clad is 1.5 times or more the mode field diameter of thewaveguide mode of the operating wavelength (1500 nm to 1600 nm in thepresent embodiment and preferably 1500 nm) of this slant SPG. There isno particular restriction as to the upper limit value; however, it ispractically set at 8 times or less.

If the above value is less than 1.5 times, because the grating portionof the photosensitive layer is not formed in the area where thewaveguide mode is propagated, there are times when sufficienttransmission loss of the waveguide mode cannot be obtained.

Once these conditions have been satisfied it is desirable that the outerdiameter of the photosensitive layer of the clad is 60 μm or less.

Because there is a tendency for the photosensitive layer to absorb lightof a specific wavelength that is irradiated thereon during formation ofthe grating, if the outer diameter of the photosensitive layer is toolarge, when light is irradiated from the side surface of the opticalfiber, sufficient light is not irradiated onto the portion of thephotosensitive layer located on the opposite side to the lightirradiation surface, and it is not possible for the refractive index tobe raised sufficiently and, in some cases, the change in the refractiveindex is not uniform.

It is desirable that the grating length is between 1 and 100 mm. If itis less than 1 mm, then there is the concern that it is too short andthe required transmission loss will not be obtained. If the gratinglength exceeds 100 mm, then not only are there difficulties in theformation of the grating portion, but the size of the device increases,which will cause problems when the device is housed in a module or thelike.

Because the grating length has an effect on the optical characteristicssuch as the frequency band loss and the like, it is preferable that thegrating length is suitably adjusted while considering the desiredcharacteristics.

Providing the clad is provided with a photosensitive layer, this may beone layer or may be a multilayered structure formed from two or morelayers, however, from the viewpoint of manufacturability, a multilayeredstructure of two or more layers is preferable. Furthermore, it ispossible to alter as is appropriate conditions such as the dopingamounts of photosensitive dopant and dopant for adjusting the refractiveindex in accordance with the design conditions. Moreover, in the presentembodiment it is possible to manufacture the optical fiber used in theslant SPG by a known method such as the VAD method, the MCVD method, thePCVD method, or the like. The grating portion may be manufactured by aknown method using an excimer laser or the like as the light source.

The standardized frequency V and the theoretical cutoff wavelength λccan be represented by Formula (5) below. $\begin{matrix}{\lambda_{c} = {\frac{V}{Vc}\lambda}} & (5)\end{matrix}$

In Formula (5) λc is the theoretical cutoff wavelength, Vc is aconstant, namely, 2.4048256, and λ is the operating wavelength and inthe present embodiment is, for example, between 1,500 and 1,600 nm, andis preferably 1,550 nm.

Accordingly, if the value of λc is determined by substituting the valuesfor the standardized frequency V and the like in Formula (5), then it ispossible to describe the conditions for the present invention using λcinstead of the standardized frequency V.

Note that in many cases the cutoff wavelength of an actual slant SPG isevaluated not using the theoretical λc, but using an execution cutoffwavelength. The execution cutoff wavelength is determined by JIS C 6825,Section 8.2.3 and is a shorter value than the theoretical cutoffwavelength.

Note also that, in accordance with the above procedure, if a slant SPGis designed so that the conditions of at least one (preferably two ormore and most preferably three) of Formulas (2) to (4) are satisfied,and this slant SPG manufactured, then it is possible to reliably obtaina slant SPG having the desired characteristics.

3. Concerning Slant SPG Applications:

Because the slant SPG of the first or second embodiment is a slant typeof short-period grating, it has the advantage of little reflected light.Furthermore, by selecting the conditions, smooth spectrumcharacteristics with a narrow frequency band can be obtained. Moreover,by combining the above conditions it is possible to design SPG having avariety of optical characteristics.

Therefore, the present invention can be preferably applied to a gainequalizer that equalizes the wavelength dependency of the gain of anoptical amplifier, and to construct an optical amplifier module providedwith this optical amplifier and gain equalizer.

An Er doped optical fiber amplifier that uses an Er doped optical fiberis preferably used as the optical fiber amplifier because of itssuitability for amplifying optical signals in the vicinity of the 1,550nm wavelength.

Note that, conventionally, a long period grating or etalon or the likeis used for this gain equalizer. For example, a plurality of long periodgratings that each have light loss characteristics in a differentwavelength region and that are connected in series are used to form again equalizer.

An optical fiber amplifier module is constructed by combining an Erdoped optical fiber amplifier with the above type of gain equalizer.

Note that the loss peak that can be obtained using a single long periodgrating has a substantially triangular bell shape. Therefore, in thewavelength spectrum of the gain equalizer, a loss peak whoseconfiguration is composed of a plurality of narrow, substantiallytriangular peaks arranged in a row is obtained.

Accordingly, in the wavelength spectrum of light transmitted through anoptical fiber amplifier module, what is known as gain residue, which iswhere the gain was not able to be flattened, is present between theplurality of loss peaks.

There is also an optical communication system used for long distancetransmissions in which a plurality of the above type of optical fiberamplifier modules are connected in series in multiple stages.

Note that an optical communication system is provided, at one endportion thereof, with a transmitting portion that emits optical signalsand, at the other end portion thereof, with a receiving section thatreceives optical signals. An optical amplifier module is inserted intothe optical transmission path connecting the transmitting portion andthe receiving portion.

The gain residue that is generated by the transmission through each ofthe optical fiber amplifier modules forming this system is present inthe respective same wavelength frequency bands.

Accordingly, the gain residue accumulates due to the transmissionthrough each of the optical fiber amplifier modules and the transmissioncharacteristics are affected.

Therefore, conventionally, an intensive equalizer is inserted every 10to 20 optical fiber amplifier modules so as to remove the accumulatedgain residue. This has caused problems with the cost of the device.

However, the slant SPG of the present invention enables an arbitrarytransmission loss to be obtained compared with when an LPG is used.Therefore, if an optical fiber amplifier module is constructed bycombining, for example, an Er doped optical fiber amplifier with theslant SPG of the present invention, then it is possible to equalize thegain of an Er doped optical fiber amplifier even more accurately, and toreduce gain residue.

As a result, it is possible to greatly reduce the number of intensivegain equalizers, thereby enabling a lowering in the cost of this opticalcommunication system to be achieved.

Note that the wavelength frequency band of an Er doped optical fiberamplifier that requires gain equalization is between 10 nm and 45 nm.

Furthermore, the frequency band where a loss peak of a slant SPG with afixed grating period may, for example, be between 5 nm and 10 nm.

In order to broaden this to the range of the 10 to 45 nm gainequalization frequency band of the Er doped optical fiber amplifier, itis preferable that a chirped pitch and fine adjustment be employed. Itis sufficient if the chirping ratio is larger than 0, and, because ofthe gain equalization frequency band and the grating length, preferablynot more than 20 nm/cm. Moreover, from the viewpoint of controllabilityof the filter configuration (i.e., the configuration of the loss peak),it is preferable if the chirping ratio is essentially 0.2 nm/cm or more.

This type of optical amplifier module can be applied to various opticalcommunication systems. For example, when long distance wavelengthdivision multiplexing is performed using dispersion shifted opticalfibers and the like, this optical amplifier module can be applied to anoptical communication system or the like by being inserted partway alongthe transmission path, and performing optical communication whileamplifying the optical signal.

Industrial Applicability

As has been described above, by means of the present invention it ispossible to provide a slant SPG which, in the wavelength spectrum oftransmitted light, has a narrow loss frequency band, has reduced ghostmode peaks, and enables a reduction in side band transmission loss to beachieved.

As a result, because the free design of optical characteristics becomespossible, the present invention can be used to adjust the opticalcharacteristics of various optical devices such as Er doped opticalfiber amplifiers.

What is claimed is:
 1. A slant short-period grating which is obtainableby irradiating light onto an optical fiber having a core and a cladprovided on an outer periphery of the core, the core being formed fromquartz glass to which has been doped a photosensitive dopant thatchanges a refractive index of the quartz glass by light irradiation, andthe clad having one or two or more layers with at least the layer thatis adjacent to the core being a photosensitive layer formed from quartzglass to which has been doped a photosensitive dopant that changes arefractive index of the quartz glass by light irradiation, and thereby agrating portion is formed by changing the refractive index of thephotosensitive layer of the clad and the core at a predetermined gratingperiod along a longitudinal direction of the optical fiber by apredetermined slant angle, wherein a diameter of the core is 5 μm ormore; wherein a relative photosensitivity ratio of the core relative tothe photosensitive layer of the clad that is adjacent to the coresatisfies Formula (1) below:0.2−0.1·(V−1.7)≦P≦0.1a{0.41−0.33·(V−1.7)}  (1) in Formula (1), a is thediameter of the core in units of μm, V is a standardized frequency, andP is the relative photosensitivity ratio of the core relative to thephotosensitive layer of the clad that is adjacent to the core; andwherein the slant angle is set to such an angle that loss due tocoupling of a waveguide mode with a reflection mode is minimum.
 2. Aslant short-period grating according to claim 1, wherein the diameter ofthe core is 7 μm or more.
 3. A slant short-period grating according toclaim 1, wherein the relative photosensitive ratio of the core is 0.1 to0.4.
 4. A slant short-period grating according to claim 1, wherein anouter diameter of the photosensitive layer of the clad is four times ormore the size of the diameter of the core.
 5. A slant short-periodgrating according to claim 1, wherein the diameter of the core is 12 μmor less.
 6. A slant short-period grating according to claim 1, wherein acomparative refractive index difference between the core and the clad is0.5% or less.
 7. A slant short-period grating according to claim 1,wherein aluminum or phosphorous is doped to the core.
 8. A slantshort-period grating which is obtainable by irradiating light onto anoptical fiber having a core and a clad provided on an outer periphery ofthe core, the clad having one or two or more layers with at least onelayer being a photosensitive layer formed from quartz glass to which hasbeen doped a photosensitive dopant that changes a refractive index ofthe quartz glass by light irradiation, and thereby a grating portion isformed by changing the refractive index of the photosensitive layer at apredetermined grating period along a longitudinal direction of theoptical fiber by a predetermined slant angle, wherein a relativephotosensitivity ratio of the core relative to the photosensitive layerof the clad that has the highest photosensitivity satisfies Formula (2)below: P≦m ₁ (V−2 )+m ₂ m ₁=0.0041667a ⁴−0.13519a ³+1.6206a²−8.511a+16.291   (2) m ₂=−0.0083827a ²+0.18344a−0.6912 however, when Pequals 0 or smaller or is imaginary number, P is 0 in Formula (2), a isthe diameter of the core in units of μm, V is a standardized frequency,and P is the relative photosensitivity ratio of the core relative to thephotosensitive layer of the clad that has the highest photosensitivity.9. A slant short-period grating which is obtainable by irradiating lightonto an optical fiber having a core and clad provided on an outerperiphery of the core, the clad having one or two or more layers with atleast one layer being a photosensitive layer formed from quartz glass towhich has been doped a photosensitive dopant that changes a refractiveindex of the quartz glass by light irradiation, and thereby a gratingportion is formed by changing the refractive index of the photosensitivelayer at a predetermined grating period along a longitudinal directionof the optical fiber by a predetermined slant angle, wherein a relativephotosensitivity ratio of the core relative to the photosensitive layerof the clad that has the highest photosensitivity satisfies Formula (3)below: P≧(V−1.7868)^(0.048522)+0.17416V−1.121  (3) however, when Pequals 0 or smaller or is imaginary number, P is 0 in Formula (3), a isthe diameter of the core in units of μm, V is a standardized frequency,and P is the relative photosensitivity ratio of the core relative to thephotosensitive layer of the clad that has the highest photosensitivity.10. A slant short-period grating which is obtainable by irradiatinglight onto an optical fiber having a core and clad provided on an outerperiphery of the core, the clad having one or two or more layers with atleast one layer being a photosensitive layer formed from quartz glass towhich has been doped a photosensitive dopant that changes a refractiveindex of the quartz glass by light irradiation, and thereby a gratingportion is formed by changing the refractive index of the photosensitivelayer at a predetermined grating period along a longitudinal directionof the optical fiber by a predetermined slant angle, wherein a relativephotosensitivity ratio of the core relative to the photosensitive layerof the clad that has the highest photosensitivity satisfies Formula (4)below: P≧m1 (a−m2)^(m3) m1=−0.28947+0.17702V m2=−344.28+543.53V−272.8V²+44.494V ³  (4) m3=0.96687−0.24791V however, when P equals 0 or smalleror is imaginary number, P is 0 in Formula (4), a is the diameter of thecore in units of μm, V is a standardized frequency, and P is therelative photosensitivity ratio of the core relative to thephotosensitive layer of the clad that has the highest photosensitivity.11. A slant short-period grating according to any of claims 8 to 10,wherein the slant angle is set such that loss due to coupling of awaveguide mode with a reflection mode is minimum.
 12. A slantshort-period grating according to any of claims 8 to 10, wherein therelative sensitivity ratio of the core relative to the photosensitivelayer is 0.2 or more.
 13. A slant short-period grating according to anyof claims 8 to 10, wherein the grating period is a chirped pitch, andthe chirping ratio of the grating period is 20 nm/cm or less.
 14. Aslant short-period grating according to any of claims 1 to 10, wherein abend loss of the optical fiber in conditions of a wavelength of 1,550 nmand a winding diameter of 60 mm is 1 dB/m or less.
 15. A slantshort-period grating according to any of claims 1 to 10, wherein a bendloss of the optical fiber in conditions of a wavelength of 1,550 nm anda winding diameter of 40 mm is 0.1 dB/m or less.
 16. A slantshort-period grating according to any of claims 1 to 10, wherein a modefield diameter of a waveguide mode of the optical fiber in an operatingwavelength of the slant short-period fiber grating is 15 μm or less. 17.A slant short-period grating according to any of claims 1 to 10, whereinthe outer diameter of the photosensitive layer is 1.5 times or more thesize of the mode field diameter of a waveguide mode of the optical fiberin an operating wavelength of the slant short-period fiber grating. 18.A slant short-period grating according to any of claims 1 to 10, whereinthe outer diameter of the photosensitive layer is 60 μm or less.
 19. Aslant short-period grating according to any of claims 1 to 10, whereinthe length of the grating portion is 1 to 100 mm.
 20. An opticalamplifier module comprising the slant short-period grating according toany of claims 1 to 10 and an optical amplifier, wherein gainequalization of the optical amplifier is performed by the slantshort-period grating.
 21. An optical amplifier module according to claim20, wherein the optical amplifier is an erbium doped optical fiberamplifier.
 22. An optical communication system that employs the opticalamplifier module according to claim
 20. 23. A method for manufacturing aslant short-period grating in which a slant short-period grating isdesigned and manufactured such that the conditions described in any ofclaims 1 to 10 are satisfied.